The ubiquitous usages of smartphones demand reliable mobile authentication systems, which are expected to play an indispensable role in protecting users' sensitive and private information. Among various mobile authentication mechanisms, face authentication (FA) has become the most popular choice on modern smartphones, owing to its excellent performance and user experience. Unfortunately, emerging advanced attacks have brought in severe security concerns against FA systems (e.g., privacy leakage, property damage), which have also triggered increased attention on face anti-spoofing designs. This paper provides a concise review of the advanced face anti-spoofing systems over smartphones from a practical perspective. We first review the presentation attacks (PAs) toward FA systems and classify them according to the geometry and dynamic property of the presentation mediums. Then we survey the state-ofthe- art presentation attack detection (PAD) approaches over smartphones and categorize these methods into four categories based on the cues they leverage. Furthermore, we present a comprehensive comparison of their advantages and disadvantages from various practical aspects. Finally, we provide recommendations for future directions. We hope our viewpoints would shed light on potential pathways for more reliable FA in the future.